Particle Filter for Robot Localization

Vuk Malbasa

Problem

• Map is given as bitmap

• It is possible to measure distance to dark like from any position

• Robot needs to find out where on the map it is located

• Only available data is:

• Odometry (noisy)

• Range finding (noisy)

• Robot is programmed to follow a particular route around the map and is allowed to measure at each time step

Robot sensors• The robot measures distance to wall from

several directions– I assumed that a gyroscope would always let

the robot take measurements from the same angle

• Additive noise is simulated in the measurements as

ε ~ N(0,1)

• The robot sees a vector of distances

• To localize the robot needs to find a spot on the map which has similar distances to what it sees

• The measure of similarity– Given the current robot measurements as the

mean of a normal distribution with a large standard deviation how likely are the measurements taken from different locations across the map?

R

Measurements• Sometimes the measurements can be

ambiguous• When there the robot is in a repetitive

position on the map the distance function can be deceiving– This is where odometry helps

• When in the features that the robot sees are unique to that position on the map then the distance function has one optimum

Measurements• When the map is complex and the

measurements are noisy then the distance function shows multiple optima

• This leads to the importance of keeping track of previous positions of particles

– While a positions measurements may not be unique to a particular place on the map, the sequence of measurements is unique

Algorithm

initialize particles

for i = 1:length(movement)

take measurements from current position

simulate measurements for particles

calculate distance function

assign weights

resample

move robot

move particles

end

PracticeAt the beginning of the movement there are many possible positions because of noisy measurements and the wide Gaussian distance function

After a few iterations there are only two major positions left and the biggest one is wrong

However once the robot moves into a place on the map with unique measurements there is only one position

Parallel to evolutionary computation

loop

predict

evaluate

resample

end

loop

simulate

evaluate

reproduce

end

Particle filters Evolutionary Computation

Uncanny similarity